Abstract
A novel integrated sustainability index (ISI) and a related criticality index (CI) are proposed to assess the performance of nodes in a water distribution network (WDN). The ISI integrates information discerned from two hydraulic indicators (reliability and redundancy) and a topological measure (closeness centrality), which are critical for defining WDN performance. The hydraulic indicators focus on demand satisfaction with desired pressure at nodes, whereas topologic measures account for the interdependencies and interconnectedness of the network components. The CI aids in differentiating nodes with similar hydraulic or topologic characteristics to identify the most critical nodes in a WDN, whose maintenance and management are essential to ensure the smooth operation of the network. The potential of ISI over the conventional hydraulic indicators-based sustainability index and efficacy of the CI over five existing indices (betweenness centrality, closeness centrality, eigenvector centrality, demand centrality, and demand-adjusted entropic degree) is illustrated through case studies on one hypothetical and two real networks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Agathokleous A, Christodoulou C, Christodoulou SE (2017) Topological robustness and vulnerability assessment of water distribution networks. Water Resour Manage 31(12):4007–4021. https://doi.org/10.1007/s11269-017-1721-7
Alessandro P, Giordano R, Portoghese I (2022) A pipe ranking method for water distribution network resilience assessment based on graph-theory metrics aggregated through Bayesian belief networks. Water Resour Manage 36(13):5091–5106. https://doi.org/10.1007/s11269-022-03293-z
Awumah K, Goulter I, Bhatt SK (1990) Assessment of reliability in water distribution networks using entropy based measures. Stoch Hydrol Hydraul 4(4):309–320. https://doi.org/10.1007/BF01544084
Awumah K, Goulter I, Bhatt SK (1991) Entropy-based redundancy measures in water-distribution networks. J Hydraul Eng 117(5):595–614. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(595)
Aydin NY, Mays L, Schmitt T (2014) Sustainability assessment of urban water distribution systems. Water Resour Manage 28(12):4373–4384. https://doi.org/10.1007/s11269-014-0757-1
Bao Y, Mays L (1990) Model for water distribution system reliability. J Hydraul Eng 116(9):1119–1137. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:9(1119)
Borgatti SP (2005) Centrality and network flow. Social Networks 27(1):55–71. https://doi.org/10.1016/j.socnet.2004.11.008
Cadini F, Zio E, Petrescu CA (2009) Using centrality measures to rank the importance of the components of a complex network infrastructure. In Critical Information Infrastructure Security: Third International Workshop, CRITIS 2008, Rome, Italy, October13–15, 2008. https://doi.org/10.1007/978-3-642-03552-4_14
Dunn S, Wilkinson SM (2013) Identifying critical components in infrastructure networks using network topology. J Infrastruct Syst 19(2):157–165. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000120
Giustolisi O, Ridolfi L, Simone A (2019) Tailoring centrality metrics for water distribution networks. Water Resour Res 55(3):2348–2369. https://doi.org/10.1029/2018WR023966
Gupta R, Baby A, Arya PV, Ormsbee L (2014) Segment-based reliability/supply short fall analysis of water distribution networks. Procedia Eng 89:1168–1175. https://doi.org/10.1016/j.proeng.2014.11.244
Gupta R, Bhave PR (1994) Reliability analysis of water-distribution systems. J Environ Eng 120(2):447–460. https://doi.org/10.1061/(ASCE)0733-9372(1994)120:2(447)
Hashimoto T, Stedinger JR, Loucks DP (1982) Reliability, resiliency, and vulnerability criteria. Water Resour Res 18(1):14–20. https://doi.org/10.1029/WR018i001p00014
Jaewoo S, Kim I, Park J (2023) Random Network Model for Assessing the Topological Performance of Water Distribution Systems. KSCE J Civ Eng 27(10):4101–4114. https://doi.org/10.1007/s12205-023-1318-z
Jung D, Kang D, Kim JH, Lansey K (2014) Robustness-based design of water distribution systems. J Water Resour Plan Manag 140(11):1–14. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000421
Lee S, Kim JH (2020) Quantitative measure of sustainability for water distribution systems: a comprehensive review. Sustainability 12(23):1–19. https://doi.org/10.3390/su122310093
Li Y, Yang ZF (2011) Quantifying the sustainability of water use systems: calculating the balance between network efficiency and resilience. Ecol Model 222(10):1771–1780. https://doi.org/10.1016/j.ecolmodel.2011.03.001
Loucks DP (1997) Quantifying trends in system sustainability. Hydrol Sci J 42(4):513–530. https://doi.org/10.1080/02626669709492051
Mohsen H, Yousefi A, Hesarkazzazi S, Minaei A, Jenewein O, Shahandashti M, Sitzenfrei R (2023) Resilience enhancement of water distribution networks under pipe failures: a hydraulically inspired complex network approach. AQUA – Water Infrastruct, Ecosyst Soc 72(12):2358–2376. https://doi.org/10.2166/aqua.2023.180
Newman (2010) Network an introduction, Vol. 66. Oxford University Press, Oxford
Ostfeld A (2004) Reliability analysis of water distribution systems. J Hydroinf 6(4):281–294. https://doi.org/10.2166/hydro.2004.0021
Rochat Y (2009) Closeness centrality extended to unconnected graphs: the harmonic centrality index. In: Applications of Social Network Analysis (ASNA), Zürich, 1–15. https://infoscience.epfl.ch/record/200525?ln=en
Sandoval-Solis S, McKinney DC, Loucks DP (2011) Sustainability index for water resources planning and management. J Water Resour Plan Manag 137(5):381–390. https://doi.org/10.1061/(ASCE)wr.1943-5452.0000134
Savic DA, Walters GA (1997) Evolving sustainable water networks. Hydrol Sci J 42(4):549–564. https://doi.org/10.1080/02626669709492053
Simone A, Ridolfi L, Laucelli DB et al (2018) Centrality metrics for water distribution networks. EPiC Series Eng 3:1979–1988
Sirsant S, Reddy MJ (2020) Assessing the performance of surrogate measures for water distribution network reliability. J Water Resour Plan Manag 146(7):1–15. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001244
Tanyimboh TT (2017) Informational entropy: a failure tolerance and reliability surrogate for water distribution networks. Water Resour Manage 31(10):3189–3204. https://doi.org/10.1007/s11269-017-1684-8
Tanyimboh TT, Czajkowska AM (2021) Entropy maximizing evolutionary design optimization of water distribution networks under multiple operating conditions. Environ Syst Decisions 41(2):267–285. https://doi.org/10.1007/s10669-021-09807-1
Xu C, Goulter I (1999) Reliability-based optimal design of water distribution networks. J Water Resour Plan Manag 125(6):352–362. https://doi.org/10.1061/(ASCE)0733-9496(1999)125:6(352)
Yazdani A, Jeffrey P (2011) Complex network analysis of water distribution systems. Chaos An Interdisciplinary Journal of Nonlinear Science 21(1). https://doi.org/10.1063/1.3540339
Yazdani A, Jeffrey P (2012) Water Distribution System Vulnerability Analysis Using Weighted and Directed Network Models. Water Resour Res 48(6):1–10. https://doi.org/10.1029/2012WR011897
Yumin W, Zhu G (2022) Hydraulic and Water Quality Reliability of Water Distribution System under Uncertain Conditions. J Pipeline Syst Eng Practice 13(4):04022035. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000676
Zarghami SA, Gunawan I (2020) A domain-specific measure of centrality for water distribution networks. Eng Constr Archit Manag 27(2):341–355. https://doi.org/10.1108/ECAM-03-2019-0176
Acknowledgements
The authors acknowledge the Associate Editor and three reviewers for providing useful remarks/suggestions, which helped in improving the manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical Approval
All authors kept the “Ethical Responsibilities of Authors”.
Consent to Participate
All authors gave explicit consent to participate in this study.
Consent to Publish
All authors agree to publish.
Competing Interests
The authors declare no conflicts of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pandey, J., Srinivas, V.V. Integrated Sustainability Index for Assessing the Performance of Water Distribution Network. Water Resour Manage (2024). https://doi.org/10.1007/s11269-024-03835-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11269-024-03835-7